Is $3 − 2i$ irreducible in $\mathbb Z[i]$?

Question

I know in order to be irreducible $3-2i$ must not equal zero, it's not a unit and whenever $3-2i=ab$ then either $a$ is a unit or $b$ is a unit. We can assume $3-2i=(a+bi)(c+di)$ for some $a,b,c,d$ in the integers and both elements are not units. After this I am not sure where to proceed.

Answer 1

HINT: $|3-2i|^2 = 13$ is prime.